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Computational Cognitive Science

Computational Cognitive Science 10
Introduction Modeling Working Memory Basic Modeling Concepts Computational Cognitive Science Lecture 2: Basic Model Building Frank Keller School of Informatics University of Edinburgh kellerinf.ed.ac.uk September 23, 2016 Frank Keller Computational Cognitive Science 1Introduction Modeling Working Memory Basic Modeling Concepts 1 Introduction 2 Modeling Working Memory 144 Models of Working Memory Fixed Decay Variable Decay 3 Basic Modeling Concepts Parameters Discrepancy Function Reading: Lewandowsky and Farrell (2011: Ch. 2). Frank Keller Computational Cognitive Science 2Introduction Modeling Working Memory Basic Modeling Concepts Working Memory Working memory allows us to brie y remember chunks of information (phone numbers, names, faces). A standard account of working memory is Baddeley's (1986) model. Here, we will focus on the phonological loop in his model: information in the loop decays rapidly over time; memory content can be refreshed by articulatory rehearsal; rehearsal is subject to articulatory suppression: when irrelevant material is spoken during encoding, recall is worse. Memory models are often tested in recall experiments in which participants see lists of words, memorize them, and then recall them as accurately as possible. Frank Keller Computational Cognitive Science 3Introduction Modeling Working Memory Basic Modeling Concepts Working Memory Frank Keller Computational Cognitive Science 4Introduction Modeling Working Memory Basic Modeling Concepts Working Memory Word length e ect (WLE): shorter words are recalled better than long ones (higher speech rate equals shorter word length); explanation: short words can be rehearsed more often in the same amount of time in the phonological loop. Frank Keller Computational Cognitive Science 5Introduction Modeling Working Memory Basic Modeling Concepts Working Memory The phonological loop explains the WLE and many other ndings in the memory literature. However, the loop is not necessary or sucient for the WLE: long words di er from short words in many ways (number of syllables, frequency), so duration may not be the key factor; alternative models without decay can also predict the e ect. Another key problem is that Baddeley's account is at the level of a verbal theory. There are many possible ways to instantiate this theory in a computational model. Frank Keller Computational Cognitive Science 6Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay 144 Models of Working Memory To arrive at an implementable model, we need to clarify a number of key assumption in the verbal theory: How is order encoded How do we make sure that items are rehearsed and recalled in the correct order What is it that decays It can't be the actual knowledge of words (that's in longterm memory). What kind of representations do we assume (distributed vs. localized) In addition to this, we face a number of technical issues regarding how to implement rehearsal and decay. Frank Keller Computational Cognitive Science 7Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay 144 Models of Working Memory There is a space of 144 possible models based on the following implementation decisions: Decisions Point N Alternatives Our Decision (1) Begin of decay 2 After list (2) Decay function 3 Linear (3) Decay rate 2 Constant (4) Recall success 2 Threshold (5) Recall errors 3 Omission only (6) Rehearsal sequence 2 Ordered Not all of the models capture the data. Frank Keller Computational Cognitive Science 8Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay 144 Models of Working Memory 1 Decay begins once the presentation of the word list is nished, not at each individual word. 2 Decay is linear (rather than exponential or powerlaw). 3 Decay is constant, i.e., the same for each item for each participant (rather than variable). 4 Recall is thresholded, i.e., once the activation of an item falls below a certain value, it is forgotten. 5 Recall errors can only include omissions (items are forgotten), not items in the wrong order or items that were not in the list. 6 Rehearsal is ordered, it consists of a recall of the complete list in the order of presentation. These decisions are often motivated by the need to keep the implementation tractable. Frank Keller Computational Cognitive Science 9Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay Matlab Implementation Variable initialization: clear all nReps = 1000; number of replications listLength = 5; number of list items initAct = 1; initial activation of items dRate = .8; decay rate (per second) delay = 5; retention interval (seconds) minAct = .0; minimum activation for recall Frank Keller Computational Cognitive Science 10Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay Matlab Implementation The main loop: rRange = linspace(1.5,4.,15); tRange = 1./rRange; pCor = zeros(size(rRange)); i=1; index for word lengths for tPerWord=tRange for rep=1:nReps actVals = ones(1,listLength)initAct; ... pCor(i) = pCor(i) + (sum(actValsminAct)./listLength); end i=i+1; end Frank Keller Computational Cognitive Science 11Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay Matlab Implementation rRange: speech rates from 1.5 to 4.0 (15 values); tRange: time it takes to pronounce the items; pCor: percentage correct for each speech rate; tPerWord=tRange: iterates through the speech rates; rep=1:nReps: iterates through the rehearsals; actVals: activation values; initialized to initAct; sum(actValsminAct): determines which items have an activation above minAct, computes percentage correct. Frank Keller Computational Cognitive Science 12Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay Fixed Decay The core: rehearsal and xed decay: cT = 0; itemReh = 0; start rehearsal with beginning of list while cT delay intact = find(actValsminAct); find the next item still accessible itemReh = find(intactitemReh, 1); rehearse or return to beginning of list if isempty(itemReh) itemReh=1; end actVals(itemReh) = initAct; everything decays actVals = actVals (dRate.tPerWord); cT=cT+tPerWord; end Frank Keller Computational Cognitive Science 13Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay Fixed Decay cT: current time; intact: extract all item that are accessible (activation higher than minAct); itemReh: nd the next intact item to rehearse; set its activation to initAct; then decay all items (actVals) by dRate; move on to the next word; tPerWord is the word duration; continue until all the rehearsal time (delay) is used up. Note that rehearsal and decay take place at the same time; cT is advanced explicitly only at the end of the loop. Frank Keller Computational Cognitive Science 14Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay Fixed Decay Frank Keller Computational Cognitive Science 15Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay Modeling Result Accuracy increases with speech rate, just as in the experimental data; however, the increase is discontinuous; discontinuity follows from forgetting of individual items when they fall below threshold; items can fall below threshold if they decay because the other items on the list take too long to rehearse. Frank Keller Computational Cognitive Science 16Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay Variable Decay If we assume xed decay then small variations in speech rate are either ampli ed or nulli ed (above or below threshold), leading to a step function. Solution: add random component to decay (in second forloop): decRate = .8; mean decay rate (per second) decSD = .1; standard deviation of decay rate ... dRate = decRate+randndecSD; Frank Keller Computational Cognitive Science 17Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay Variable Decay Frank Keller Computational Cognitive Science 18Introduction 144 Models of Working Memory Modeling Working Memory Fixed Decay Basic Modeling Concepts Variable Decay Limitations and Extensions Baddeley's phonological loop model can be implemented and predicts the word length e ect. Possible extensions: exponential decay instead of linear decay; introduce mechanisms that explain transpositions (items in recalled in wrong position) and intrusions (items recalled that weren't there during training); explore the e ect of the order in which items are rehearsed (primacy e ect). Frank Keller Computational Cognitive Science 19Introduction Parameters Modeling Working Memory Discrepancy Function Basic Modeling Concepts Parameters The behavior of a model is governed by parameters such as initAct, dRate, minAct. For instance, if we decrease dRate, the model will forget less. For dRate = 0, speech rate no longer matters for recall. We normally use  to denote a parameter vector. The more parameters a model contains, the more exible it is in tting the data we're trying to model. Frank Keller Computational Cognitive Science 20Introduction Parameters Modeling Working Memory Discrepancy Function Basic Modeling Concepts Types of Parameters Free parameters such as dRate: can be adjusted until the predictions are in line with the data; the process of adjusting free parameters is called parameter estimation; the resulting estimates are the best tting parameters. Fixed parameters such as minAct: are invariant across data sets, they are built into the model architecture; increasing their number is less problematic, as it doesn't improve model t. Frank Keller Computational Cognitive Science 21Introduction Parameters Modeling Working Memory Discrepancy Function Basic Modeling Concepts Discrepancy Function Parameter estimation tries to minimize the discrepancy between model predictions and data. For this we need a discrepancy function (objective function, cost function, error function). Example: root mean squared deviation (RMSD): s P J 2 (d p ) j j j=1 RMSD = J where J is the number of data points, d are the data points, and j p are the model predictions for the data points. j Frank Keller Computational Cognitive Science 22Introduction Parameters Modeling Working Memory Discrepancy Function Basic Modeling Concepts Discrepancy Function Frank Keller Computational Cognitive Science 23Introduction Parameters Modeling Working Memory Discrepancy Function Basic Modeling Concepts Discrepancy Function If a model makes categorical predictions, other discrepancy functions are more appropriate: J 2 X (O N p ) j j 2  = N p j j=1 J X 2 G = 2 O logfO=(N p )g j j j j=1 where J is the number of categories, N the total number of responses, and O the number of responses in category j, and p j j the model prediction for category j (a probability). Next lecture: parameter estimation algorithms. Frank Keller Computational Cognitive Science 24Introduction Parameters Modeling Working Memory Discrepancy Function Basic Modeling Concepts Summary Models are often based on verbal theories; example: Baddeley's phonological loop model of working memory; we need to make assumptions about representations and mechanisms in order to turn them into computational models; in addition, implementational decisions need to be made; example: we get 144 versions of the phonological loop model; we saw a Matlab implementation of the model and compared it to the experimental data; key concepts in model buildings are: parameters, discrepancy functions, and parameter estimation. Frank Keller Computational Cognitive Science 25Introduction Parameters Modeling Working Memory Discrepancy Function Basic Modeling Concepts References Baddeley, Alan D. 1986. Working Memory. Oxford University Press, New York. Lewandowsky, Stephan and Simon Farrell. 2011. Computational Modeling in Cognition: Principles and Practice. Sage, Thousand Oaks, CA. Frank Keller Computational Cognitive Science 26
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